Spivak, Calculus and Answer Book to Calculus

Spivak, Calculus
4th ed. xvi + 680 pages.
Clothbound. 2008
Spivak, Combined Answer Book to Calculus, Third and Fourth editions.
ii + 448 pages.
Clothbound.  2008


Click here for selections from the Preface       Return to book list      Return to home page

Written as a textbook, Calculus is used both for theoretical calculus courses and for  "Introduction to Analysis" courses in several U.S. universities. It is also used  (in  rather larger numbers) in quite a few Canadian universities, as well as in a few universities overseas. Because of this, sales of the Answer Book, which are intended for instructors of the courses, are normally restricted. 

Calculus has also found an audience among individuals learning, or relearning, the material on their own.
(Some reader reviews may be found on the Amazon.com website.)

For errata for the 4th edition, send an email to puborperish@gmail.com. Type Errata in the subject line; no message necessary.


Part I    Prologue

                 1  Basic Properties of Numbers
                 2  Numbers of Various Sorts

Part II    Foundations

                 3 Functions
                    Appendix. Ordered Pairs
                 4  Graphs
                   Appendix 1. Vectors
                    Appendix 2. The Conic Sections
                    Appendix 3. Polar Coordinates

                 5  Limits
                 6  Continuous Functions
                 7  Three Hard Theorems
                 8  Least Upper Bounds
                   Appendix. Uniform Continuity

Part III    Derivatives and Integrals

                 9  Derivatives
                10 Differentiation
                11 Significance of the Derivative
                    Appendix. Convexity and Concavity
                12 Inverse Functions
                   Appendix. Parametric Representation of Curves
                13 Integrals
                   Appendix. Riemann Sums
                14 The Fundamental Theorem of Calculus
                15 The Trigonometric Functions
              *16 Pi is Irrational
              *17 Planetary Motion
                18 The Logarithm and Exponential Functions
                19 Integration in Elementary Terms
                   Appendix. The Cosmopolitan Integral

Part IV    Infinite Sequences and Infinite Series

                20 Approximation by Polynomial Functions
               *21 e is Transcendental
                22 Infinite Sequences
                23 Infinite Series
                24 Uniform Convergence and Power Series
                25 Complex Numbers
                26 Complex Functions
                27 Complex Power Series

Part V    Epilogue

                28 Fields
                29 Construction of the Real Numbers
                30 Uniqueness of the Real Numbers

                    Suggested Reading

From the preface:

Every aspect of this book was influenced by the desire to present calculus not merely as a prelude to but as the first real encounter with mathematics. Since the foundations of analysis provided the arena in which modern modes of mathematical thinking developed, calculus ought to be the place in which to expect, rather than avoid, the strengthening of insight with logic. In addition to developing the students' intuition about the beautiful concepts of analysis, it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions.
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